# Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with the measurements of volumes of various solid figures (three-dimensional figures) including pyramids, prisms and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

1. Triangular prism Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
2. Density of the concrete Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
3. Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
4. Height as diameter of base The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
5. The pot The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
6. Deviation of the lines Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
7. A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
8. Water level How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
9. Pool The prism-shaped pool is 2 m deep with a bottom of the isosceles trapezoid with base dimensions of 10 m and 18 m and arm legs 7 m long and 5.7 m long. During the spring cleaning, the bottom and walls of the pool must be painted. How many m2 of paint should
10. Cube cut In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
11. Collect rain water The garden water tank has a cylindrical shape with a diameter of 80 cm and a height of 12 dm. How many liters of water will fit into the tank?
12. Pilot How high is the airplane's pilot to see 0.001 of Earth's surface?
13. Perimeter of base The circumference of the base of the rotating cylinder is same as its height. What is the diameter and height of this cylinder with volume 1 liter?
14. Diameter of a cylinder The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track?
15. Volume of cone Find the volume of a right circular cone-shaped building with a height of 9 cm and a radius base of 7 cm.
16. Curved surface area CSA A cylinder 5cm high has a base radius(7/2) cm. Calculate the curved surface area.
17. Iceberg What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
18. 3d printer 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
19. Cylinder height Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
20. Volcano The crater of a volcano is approximately in the shape of a cone of a base 3.1416 sq. Mi. The crater's depth is 1500 ft. How many cubic yards of earth would be required to fill this cavity?

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